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Predictive Functional Control Based on Fuzzy Model: Design and Stability Study

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Abstract

In the paper the design methodology and stability analysis of parallel distributed fuzzy model based predictive control is presented. The idea is to design a control law for each rule of the fuzzy model and blend them together. The proposed control algorithm is developed in state space domain and is given in analytical form. The analytical form brings advantages in comparison with optimization based control schemes especially in the sence of realization in real-time. The stability analysis and design problems can be viewed as a linear matrix inequalities problem. This problem is solved by convex programming involving LMIs. In the paper a sufficient stability condition for parallel distributed fuzzy model-based predictive control is given. The problem is illustrated by an example on magnetic suspension system.

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References

  1. Bequette, B. W.: Nonlinear control of chemical processes: A review, Ind. Engrg. Chem. Res. 30 (1991), 1391???1413.

    Article  Google Scholar 

  2. Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory, SIAM, Philadelphia, PA, 1994.

    Google Scholar 

  3. Doyle, F. J., Ogunnaike, T. A., and Pearson, R. K.: Nonlinear model-based control using second-order Volterra models, Automatica 31 (1995), 697???714.

    Article  MathSciNet  MATH  Google Scholar 

  4. Figueroa, J. L.: Piecewise linear models in model predictive control, Latin Amer. Appl. Res. 31(4) (2001), 309???315.

    Google Scholar 

  5. Henson, M. A.: Nonlinear model predictive control: Current status and future directions, Computer Chem. Engrg. 23 (1998), 187???202.

    Article  Google Scholar 

  6. Kosko, B.: Fuzzy systems as universal approximators, IEEE Trans. Computers 43(11) (1994), 1329???1333.

    Article  MATH  Google Scholar 

  7. Leith, D. J. and Leithead, W. E.: Gain-scheduled and nonlinear systems: Dynamics analysis by velocity-based linearization families, Internat. J. Control 70(2) (1998), 289???317.

    Article  MATH  MathSciNet  Google Scholar 

  8. Leith, D. J. and Leithead, W. E.: Analytical framework for blended model systems using local linear models, Internat. J. Control 72(7/8) (1999), 605???619.

    Article  MathSciNet  MATH  Google Scholar 

  9. Morningred, J. D., Paden, B. E., and Mellichamp, D. A.: An adaptive nonlinear predictive controller, Chem. Engrg. Sci. 47 (1992), 755???762.

    Article  Google Scholar 

  10. Padin, M. S. and Figueroa, J. L.: Use of CPWL approximations in the design of a numerical nonlinear regulator, IEEE Trans. Automat. Control 45(6) (2000), 1175???1180.

    Article  MATH  MathSciNet  Google Scholar 

  11. ??krjanc, I. and Matko, D.: Predictive functional control based on fuzzy model for heat-exchanger pilot plant, IEEE Trans. Fuzzy Systems 8(6) (2000), 705???712.

    Article  Google Scholar 

  12. Takagi, T. and Sugeno, M.: Fuzzy identification of systems and its applications to modelling and control, IEEE Trans. Systems Man Cybernet. 15 (1985), 116???132.

    MATH  Google Scholar 

  13. Takagi, T. and Sugeno, M.: Stability method and design of fuzzy control systems, Fuzzy Sets Systems 45(2) (1992), 135???156.

    Article  Google Scholar 

  14. Tanaka, K., Ikeda, T., and Wang, H. O.: Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H ??? control theory, and linear matrix inequalities, IEEE Trans. Fuzzy Systems 4(1) (1996), 1???13.

    Article  Google Scholar 

  15. Wang, L.-X. and Mendel, J. M.: Fuzzy basis functions, universal approximation, and orthogonal least-squares learning, IEEE Trans. Neural Networks 3(5) (1992), 807???814.

    Article  Google Scholar 

  16. Wang, H. O., Tanaka, K., and Griffin, M. F.: An approach to fuzzy control of nonlinear systems: Stability and design issues, IEEE Trans. Fuzzy Systems 4(1) (1996), 14???23.

    Article  Google Scholar 

  17. Ying, H. G. C.: Necessary conditions for some typical fuzzy systems as universal approximators, Automatica 33 (1997), 1333???1338.

    Article  MathSciNet  MATH  Google Scholar 

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??krjanc, I., Bla??i??, S. Predictive Functional Control Based on Fuzzy Model: Design and Stability Study. J Intell Robot Syst 43, 283–299 (2005). https://doi.org/10.1007/s10846-005-5138-9

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  • DOI: https://doi.org/10.1007/s10846-005-5138-9

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